Question

Consider the quadratic equation x squared = 4x - 5. how many solutions does the equation have?

Answer 1

The quadratic equation has two complex solutions

Explanation:

we know that

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`x^(2)=4x-5`

Equate to cero

`x^(2)-4x+5=0`

so

`a=1\\b=-4\\c=5`

substitute in the formula

`x=\frac{4(+/-)\sqrt{-4^(2)-4(1)(5)}} {2(1)}`

`x=\frac{4(+/-)√(16-20)} {2}`

`x=\frac{4(+/-)√(-4)} {2}`

Remember that

`i^(2)=-1`

so

`x=\frac{4(+/-)2i} {2}`

`x=2(+/-)i`

therefore

The quadratic equation has two complex solutions